Short answer, I do not see anything that prevents this other than the stipulation under Frightful Presence that a successful save renders that creature immune to further activations for 24hrs.
Poking around the forums, I didn't see your specific question addressed previously (my search was by no means exhaustive), but I did see an argument made that because FP says "frightened or shaken" that it only stacks up to frightened.
This doesn't seem to be the intent, as it is clearly a legacy wording issue. If you compare the 3.x entry, it's clear that that language was a catch-all, indicating that the exact effect was detailed per the individual monster with FP...
However, as RAW arguments go concerning PFRPG, this interpretation has a leg to stand on since the default effect is also detailed in the FP description, YMMV. (the specifics being "why bother mentioning frightened at all if it's completely extraneous?")
As to the RAI of the situation:
This is potentially an unintended use. (Keep in mind if you can do this, any dragon old enough can also do it...) In some respects this smacks of a once per round ability, but given that PCs have access to other means of doing similar things (numerous options for free action intimidate, Final Embrace Horror), I'm not sure it's that out of line.
There is the school of thought that a full-attack is a single action (justifying a restriction here), but it's always seemed to require a certain level of mental gymnastics to me.
